Question: Simplify to lowest terms. $\dfrac{72}{16}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 72 and 16? $72 = 2\cdot2\cdot2\cdot3\cdot3$ $16 = 2\cdot2\cdot2\cdot2$ $\mbox{GCD}(72, 16) = 2\cdot2\cdot2 = 8$ $\dfrac{72}{16} = \dfrac{9 \cdot 8}{ 2\cdot 8}$ $\hphantom{\dfrac{72}{16}} = \dfrac{9}{2} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{72}{16}} = \dfrac{9}{2} \cdot 1$ $\hphantom{\dfrac{72}{16}} = \dfrac{9}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{72}{16}= \dfrac{2\cdot36}{2\cdot8}= \dfrac{2\cdot 2\cdot18}{2\cdot 2\cdot4}= \dfrac{2\cdot 2\cdot 2\cdot9}{2\cdot 2\cdot 2\cdot2}= \dfrac{9}{2}$